In " The Big Bang Theory", Rajesh from India is shown to be very shy and can't speak in front of Women without first drinking alcohol. But all of a Sudden, in Season 5 Episode 20, he is shown to be dating Laxmi, without any reference to his hesitation?

Without any real evidence, it is my experience that when I have noticed Rajesh talking to women, he always has a drink within reach. Most times in early episodes, it is in his hand suggesting easy writing, but lately the placement is more subtle. I always look for that drink to be within reach, or if not, back to the last place he sat or entered from. Sometimes it is necessary to count the beer bottles on table tops, etc. I cannot recall any time when it was not evident.

UPDATE: Here's a screen shot of their dinner date where her wine glass is in full view, but his is obscured by the salad bowl, but still evident

In an interview with the Hollywood Reporter, actor Kunal Nayyar talks about his character's development with regards to women, explaining that his newfound confidence is a result of his having spent the night with Penny at the end of season 4:

“What happens that night really gives him this level of confidence,”
Nayyar says. “Whether that works in his favor or doesn’t, it does give
him some self belief.” While Nayyar was mum about whether or not Raj
would romantically pursue his best friend’s ex-girlfriend, he hopes
Raj’s newfound confidence is just a small step forward for the
character who at the end of Season 4 was still only able to speak to
women with the assistance of alcohol.

“Do I hope that Raj becomes this womanizing player who can talk to
women all the time? No, I hope that he continues to grow,” Nayyar
says. “I really think if you take away a character’s obstacles then
there’s no comedy. Comedy is really based on overcoming obstacles and
if you take away that obstacle, my fear is that [Raj] would lose his
funny.”